Thermoplastic, e.g., polymer films have many commercial and domestic uses and demand for production of same continues to increase. In one manner of making such a film, e.g., a polyethylene, PET or nylon film, a molten resin is extruded in the form of a film or web, the film is then quenched and following quenching, the film is stretched in both the longitudinal and transverse directions. Commonly, the film will first be stretched longitudinally as with passage thereof through a differential spaced roller set. The longitudinally stretched film is then heated to an elevated temperature and passed through a tenter apparatus wherein transverse stretching of the film is accomplished in a stretching zone by means of tenter clips which grip the marginal edges of the film. In the tenter apparatus, the clips are conveyed along diagonal or laterally widening travel paths as they grip the edges of the film so that there is produced a corresponding lateral widening, i.e., a lateral stretching of the web from an initial web width to a final web width. The divergent travel paths which the clips follow during web lateral stretching generally will be straight lines or a composite of end-to-end arranged shorter straight lines, certain of which may be skewed to a small degree in respect of others. The overall profile appearance of these composite lines, while appearing to have a curvature aspect, represents straight line clip travel courses only and as discussed below, clip straight line travel involves application of undesirable high levels of tensile stress to the web. Representative of such tenter frame constructions are the disclosures of U.S. Pat. Nos. 3,529,332 3,727,273 and 3,916,491 also discloses a straight line laterally widening stretching course. A characteristic of this stretching of a web along straight line laterally widening paths is the creation immediately at the entry location to the stretching zone of a stretch rate condition in the web which has its maximum value at that location. If the tensile stress imposed on the web of film at this maximum value stretch rate exceeds the critical stress of the web, the web can be ruptured. The prime disadvantage of web rupture is, of course, the need to stop the film production line, clear the rupture and then restart the line. This downtime of the film manufacturing line is costly and must be avoided if the economical advantages of continuous manufacturing operations are to be realized.